If you don't meet the conditions for a reaction when (and right after) the trigger occurs, then you don't get to take the reaction.
The case you describe seems to be as follows:
- Fighter and Wizard are w/in 5' of each otherother; Wizard casts Hold Person
- Fighter fails save, is held (thus unable to take his reaction attack from mage slayer)
- Wizard does other things on his turn
- Time passes
- Fighter becomes unheld and attacks wizard for using Hold Person.
This is not permitted by the rules:
A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else’s (Player's Basic D&D p70p. 70, emphasis mine).
A reaction is instant, you can't sit on the trigger for some undetermined amount of time just because you don't qualify at that moment.
The text from Ready lends credence to this interpretation:
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger (Players Basic D&D p72p. 72, emphasis mine).
Unless otherwise specified by an ability, a reaction does not interrupt or occur in the middle of its trigger.
The reaction happens after its trigger completes, unless the description of the reaction explicitly says otherwise (Xanathar's Guide to Everything p5p. 5).
So no, the scenario you describe is not possible.